On effective determination of Maass forms from central values of Rankin-Selberg $L$-function

TL;DR

This paper demonstrates that a Hecke-Maass cusp form can be effectively identified using the central values of Rankin-Selberg L-functions with other Maass forms, providing a quantitative approach.

Contribution

It introduces a quantitative method to determine Maass forms from central L-values, advancing the understanding of their uniqueness properties.

Findings

Proves a quantitative identification result for Maass forms.

Establishes a link between central L-values and form identification.

Provides bounds and conditions for form determination.

Abstract

We address the problem of identifying a Hecke-Maass cusp form $f$ of full level from the central values of the Rankin-Selberg $L$-functions $L(1/2,f\otimes h)$ where $h$ runs through the set of Hecke-Maass eigenforms of full level. We prove a quantitative result in this direction.